1.1.3 An Example Model

An example for the concept of a first-order model .

Let's look at an example. We shall define a simple model using the vocabulary given above. Let be . This set, consisting of four items, is the domain of our little model.

Next, we must specify an interpretation function . Here's one possibility:

Note that every symbol in the vocabulary neatly corresponds to an appropriate semantic entity:

• The four names correspond to individuals.

• The two arity-1 symbols correspond to subsets of (that is, properties, or 1-place relations on ).

• The arity-2 symbol corresponds to a 2-place relation on .

Intuitively, in this model is called Mary, is called Anna, is called John and is called Peter. Both Anna and Peter are morons, while both John and Mary are therapists. Peter loves Anna and John loves Mary. But for example we also know that sadly, Anna does not love Peter and Mary does not love John.